University Lecture Series 2001; 221 pp; softcover Volume: 21 ISBN10: 0821826867 ISBN13: 9780821826867 List Price: US$36 Member Price: US$28.80 Order Code: ULECT/21
 This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3dimensional topological quantum field theory, and 2dimensional modular functors (which naturally arise in 2dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the WessZuminoWitten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and MooreSeiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advancedgraduate level. Readership Graduate students and research mathematicians interested in representation theory and mathematical physics Table of Contents  Introduction
 Braided tensor categories
 Ribbon categories
 Modular tensor categories
 3dimensional topological quantum field theory
 Modular functor
 Moduli spaces and complex modular functor
 WessZuminoWitten model
 Bibliography
 Index
 Index of notation
